Design of a Passive, Shear-Based Rotary Hydraulic Damper ......Hip joint Knee joint ! Ankle joint!...

Design of a Passive, Shear-Based Rotary HydraulicDamper for Single-Axis Prosthetic Knees

Citation Arelekatti, V. N. Murthy, Nina T. Petelina, W. Brett Johnson,Amos G. Winter, and Matthew J. Major. “Design of a Passive,Shear-Based Rotary Hydraulic Damper for Single-Axis ProstheticKnees.” Proceedings of the ASME 2018 International DesignEngineering Technical Conferences and Computers andInformation in Engineering Conference, 26-29 August, 2018,Quebec City, Quebec, Canada, ASME, 2018. © 2018 by ASME

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DESIGN OF A PASSIVE, SHEAR-BASED ROTARY HYDRAULIC DAMPER FORSINGLE-AXIS PROSTHETIC KNEES

V. N. Murthy Arelekatti, Nina T. PetelinaGlobal Engineering and Research Laboratory

Department of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, Massachusetts 02139Email:[email protected], [email protected]

W. Brett JohnsonGlobal Engineering and Research Laboratory


Cambridge, Massachusetts 02139Email: [email protected]

Amos G. Winter, VGlobal Engineering and Research Laboratory


Cambridge, Massachusetts 02139Email: [email protected]

Matthew J. MajorDepartment of Physical Medicine and Rehabilitation

Northwestern UniversityChicago, Illinois 60611

Email: [email protected]

ABSTRACT

With over 30 million people worldwide in need of assistivedevices, there is a great need for low-cost, high performanceprosthetic technologies in the developing world. A majorityof the hydraulic dampers used in prosthetic knee designs arehighly specialized, expensive, require regular maintenance, andare incompatible for use with low-cost, single-axis prostheticknees popular in developing countries. In this study, optimaldamping coefficients were computed based on a theoreticalanalysis of gait, specifically during the transition from the stanceto swing phase of human walking when a large damping torqueis needed at the knee. A novel rotary hydraulic damper prototypewas designed using high-viscosity silicone oil and a concentricmeshing of fins for shearing the oil. The prototype was validatedexperimentally to provide the desired damping torque profile.For preliminary, user-centric validation of the prototype, a gaitstudy on one above-knee amputee in India was conducted withfour different damping magnitudes. Feedback from the subjectvalidated the optimal damping torque magnitude predictedfor minimizing gait deviations and for enabling able-bodied

knee kinematics. The new rotary hydraulic damper design isnovel, passive, and compatible with low-cost, single-axis kneeprostheses.

1 INTRODUCTION

This paper presents the analysis, design, and testing ofa novel hydraulic damper for a fully passive prosthetic kneemechanism. The primary goal of this study was to create adamper design that can provide accurate control of single axisknees, allow smooth transition between stance and swing phases,and can be integrated in the popular single-axis architecture ofprosthetic knees. The overarching theme of the current researchis to design all the modules required to assemble an affordable,passive knee prosthesis which can enable able-bodied gait forabove-knee amputees in developing countries, based on the priorwork done by Narang, Arelekatti and Winter [1–8].

Proceedings of the ASME 2018 International Design EngineeringTechnical Conferences and Computers and Information in Engineering Conference

IDETC/CIE 2018August 26-29, 2018, Quebec City, Quebec, Canada

DETC2018-85962

1 Copyright © 2018 ASME

Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 01/11/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use

1.1 MotivationThere are over 30 million people worldwide in need of

prosthetic and orthotic devices, according to a recent estimateby the World Health Organization [9]. Previous studies haveestimated that there are over 230,000 above-knee amputees inIndia alone [8, 10, 11], where this research is focused. Amajority of these amputations are the result of diverse factorssuch as poor health care, unsafe conditions of work, transport,and daily lifestyles [8, 12, 13]. A few prosthetic knee jointshave been designed to meet the unique needs of amputees inthe developing world. However, many of them are yet tobe adopted at scale, due to limitations in the biomechanicalperformance, design, manufacturing processes, clinical training,and maintenance [12, 13]. Past studies have also reported thatamputation results not only in 47% of the amputees having tochange or losing their occupations, but also leads to economicdeprivation and serious social stigma [14–16], which highlightsthe urgent need for high-performance, low-cost prostheses thatcan enable able-bodied gait, increase metabolic efficiency forthe users, and mitigate socio-economic discrimination faced byamputees.

1.2 Relevant TerminologyA brief summary of the relevant terms from gait

biomechanics used in this paper are laid out briefly for theuninitiated reader (Fig. 1).

1.3 Damping in the Prosthetic Knee FunctionDamping in prosthetic knees is primarily required to

decelerate the knee flexion during the transition from the stancephase to the swing phase. This duration is the zone betweenknee angle b and c of the able-bodied gait cycle (Fig. 1C). Asmaller amount of damping is also required to control the kneeextension in the swing phase between knee angles c and a, beforethe heel-strike of the next gait cycle. At knee angle b, the kneebegins to flex in preparation for the swing phase. This flexioncontinues all the way up to the peak flexion angle c in the swingphase. In the absence of sufficient damping, the prosthetic kneecan overshoot well beyond the peak flexion of the knee requiredfor ground clearance, delaying the gait cycle duration for theamputated leg. Conversely, if the damping torque is greater thanthe optimal value, the knee doesn’t flex enough, which can forcethe amputee to employ alternative strategies to achieve groundclearance during the swing phase, such as hip-hiking, vaulting,and circumduction [19]. Such asymmetric gait patterns betweenthe able-bodied leg and the amputated leg are undesirable asthey can result in increasing energy demands [19]. Additionally,in the context of developing countries such as India, the focuson achieving able-bodied gait behavior has been shown to beone of the most important design requirements for amputees [8].Amputees repeatedly report the need for an inconspicuous gait

to mitigate the socio-economic discrimination that they face,demanding prosthetic performance that can enable able-bodiedgait kinematics [8, 11].

A wide array of prosthetic knees have been designedto provide damping control. Primarily designed foramputees in mature markets, popular knee prostheses haveincorporated fluid-based (pneumatic or hydraulic) systems,which can be controlled passively, or using programmable,microprocessor-controlled actuators [20, 21]. Affordableprosthetic knee joints, designed primarily for the developingworld, have incorporated passive friction brakes that provide

Knee

Ang

le (F

lexion

)

Gait Cycle (% time)

Stance Phase Swing Phase 0 10 20 30 40 50 60 70 80 90 100

60O

45O

30O

15O

0O

Knee

Ang

le (F

lexion

)

Gait Cycle (% time)

Stance Phase Swing Phase 0 10 20 30 40 50 60 70 80 90 100

60O

45O

30O

15O

0O

Knee

ang

le (fl

exio

n)

aFlexion

Extension

Knee flexion angle

C

A

ab

c

a

BTrunk

Hip joint

Knee joint

Ankle joint

Upper leg

Lower leg

Foot

FIGURE 1. A. The knee flexion angle is defined as the relative anglebetween the upper leg segment and the lower leg segment. The directionof knee extension is opposite to that of flexion. B. Two-dimensional,four-segment link structure to model the prosthetic leg. C. The humangait cycle of each leg is divided into the stance phase, followed by theswing phase when the foot leaves contact with the ground for clearance.The graph shows the normative knee angle kinematics through the gaitcycle (red curve), along with the standard deviation shown in greyband [17, 18]. The illustration below the horizontal axis shows thecorresponding leg trajectory through the gait cycle.

2 Copyright c© 2018 by ASME


fixed resistance during flexion [22]. The implementationof friction brakes has been achieved through the use ofbolts with adjustable tension. This technique is simple andcost effective but presents many practical challenges. Thefriction torque changes with continued usage due to wearand changing environmental conditions, such as humidity orrain [4]. Moreover, friction brakes provide constant resistance,which makes them unresponsive to changes in cadence [23].Fluid-based dampers offer smooth, cadence-based resistance.However, fluid-based dampers are more expensive, bulky, andrequire periodic maintenance to prevent oil-leaks and they havenot been tested in the harsh outdoor conditions of developingcountries such as India [22]. In order to address the limitationsof traditional fluid-based dampers, this study presents thecomputational gait analysis, design and testing of a novel rotaryhydraulic damper, which is compatible for use in low-cost,single-axis prosthetic knees. The prosthetic knee used in thisstudy was developed by Arelekatti and Winter [4]. However,the design and implementation of the damper is relevant for allsingle-axis designs of prosthetic knees.

2 Methodology2.1 Computational Modeling and Analysis of

DampingAs the first step of this study, the target knee torque required

to replicate able-bodied leg kinematics in above-knee amputeeswas identified. The kinematic data required for the analysis wasobtained from an experimental study of a below-knee amputeeusing a fully passive U-spring foot designed by Prost [24]. Inthat study, the U-spring foot was mechanically characterized,theoretically optimized, and experimentally validated to providethe closest possible replication of able-bodied leg kinematics fora below-knee amputee.

To perform the target knee torque computation, atwo-dimensional, four-segment segment model of the prostheticleg was designed (Fig. 1B) and inverse dynamics performedaccording to the methods presented by Narang et al. [1].Experimental kinematic data from a unilateral below-kneeamputee walking with a fully characterized U-spring foot wasused as an input for inverse dynamics [24]. Since the massesof prosthetic leg segments are typically lower than those ofable-bodied segments [25], the knee torque was computed forvarying inertial parameters of the upper leg (the segment betweenthe hip and the knee), the lower leg (the segment between theknee and ankle), and the prosthetic foot (Fig. 1B). The masses ofthe upper-leg, the lower-leg, and the prosthetic foot were variedbetween 25% and 100% of corresponding able-bodied values.

In the prosthetic leg model, a rotary hydraulic damper wasmodeled to engage during the transition from the stance phaseto swing phase, specifically in the zone between knee angle band c of the gait cycle (Fig. 1B). The corresponding zone for

0 1 2 3 4

Damping Coefficient (N*m/(rad/s))

0

0.2

0.4

0.6

0.8

1

R2

R2 for varying values of lower-leg mass 75%

50%

25%

100%

0 20 40 60 80 100

Gait cycle (% time)

-0.4

-0.2

0

0.2

Kn

ee T

orq

ue (

N*m

/kg

)

0 20 40 60 80 100

Gait cycle (% time)

0

10

20

30

40

50

60

70

Kn

ee A

ng

le (

deg

rees)

Tdamp

Target Knee Torque

A

B

C

FIGURE 2. A. Knee angle kinematics data for a below-knee amputeeusing the passive, U-spring foot [24]. The damping zone of interestis highlighted. B. Target knee torque for replication was computedby inverse dynamics and a best-fit analysis was done to estimate theoptimal damping torque in the damping zone, Tdamp. C. The dampingcoefficients were computed for four mass values of the lower-leg,expressed as percentage fraction of the able-bodied mass of the lowerleg. The optimal damping coefficient for each mass was chosen basedon the maximum R2 value computed over the damping zone.

the kinematic data used for the analysis is highlighted in Fig. 2A(hereby referred to as the “damping zone”). The rotary hydraulicdamper was modeled as an ideal, first-order, shear-based viscousdamping element, formulated mathematically as follows:

Tdamp =−B · θ̇knee (1)



where Tdamp is the damping torque, which is the product ofthe measured angular velocity of the knee over the damping zone,θ̇knee, and B, the damping coefficient.

A simple optimization routine was set up to compute thebest-fit damping torque profile over the damping zone. Inorder to estimate the optimal damping coefficient, the dampingtorque Tdamp profiles were computed for a range of dampingcoefficients. The damping torque profile with highest coefficientof determination (R2) with reference to the target dampingtorque was selected and the corresponding damping coefficientidentified as the optimal case (Fig. 2B).

This optimization routine was set up for a range ofcombination of mass properties of the upper leg, lower leg,and foot of the prosthetic leg. For any specific combination ofthe mass properties of the prosthetic leg, the optimal dampingcoefficient, Boptimal , could be computed. For instance, for anamputee with total body weight 75 kg, 100% upper leg mass (ofable-bodied value), 50% lower leg mass (of able-bodied value),and 100% mass of the U-spring foot, Boptimal = 1.5 N-m/(rad/s)(Fig. 2C).

2.2 The DesignThe detailed construction of the damper prototype is

illustrated in Fig. 3. The damping torque in the assembly isgenerated by shearing a highly viscous liquid between the statorand the rotor. The rotor is coupled coaxially to the rotating shaftfrom the prosthetic knee, which provides the rotary motion asthe knee flexes. The stator is coupled to the housing, which isstatic and rigidly coupled to the prosthetic knee assembly. Thestator and the rotor have concentric thin-wall fins that mesh intoeach other coaxially about the knee axis, leaving a small gapwith liquid between the neighboring fins of the stator and therotor (Fig. 3B). The resulting damping torque due to the shearingof viscous liquid between the neighboring stator-rotor fins isquantified by the following relationship, derived by integratingthe viscous shear stress caused by couette flow of the liquid alongthe circumferential area of the fin walls [26]:

B f in =Tdamp

θ̇knee=

2πµht

(R31 +(R1 −w)3) (2)

where B f in is the resultant damping coefficient, Tdamp is theviscous damping torque, θ̇knee is the angular velocity of the kneejoint, µ is the dynamic viscosity of the fluid, h is the height ofthe fins, t is the thickness of the gap between the stator fin androtor fin , R1 is the radius of the exterior surface of the fin, and wis the thickness of the fin wall. These variables are annotated inFig. 3B.

The total damping torque for multiple fins, as illustrated inFig. 3, is a summation:

w

tknee flexion

R1

shaft seal

h

one-way

roller clutch

housing stator

rotor

A

B

C

FIGURE 3. A. Damper Prototype assembly: CAD and photograph ofthe final assembly. The stator and rotor fins were 3D printed in red ABSplastic. B. Cross sectional view of the damper prototype, silicone oil isentrapped between the rotor and stator fins. C. The damper was mountedcoaxially to the prosthetic knee assembly, as shown. The housing capwas bolted on to the side of the prosthetic knee structure.

Btotal =Tdamp

θ̇knee=

n

∑i=1

2πµht

((R1−(i−1)D)3+(R1−w−(i−1)D)3)

(3)

D = 2(w+ t) (4)



where n is the total number of fins on either the stator or therotor and D is the step distance to the next set of interacting fins,n = 3 in Fig. 3B.

The housing and the housing cap of the damper prototypewere machined out of Delrin. The stator and rotor fins were 3Dprinted using ABS plastic (Fig. 3A). The rotor was coupled to aone-way roller clutch, which in turn was coupled to the rotatingknee shaft (Fig. 3B). The one-way roller clutch ensures thatdamping is enabled only within the damping zone. During kneeextension, there was no damping and the knee shaft rotated freelywithin the roller clutch. The viscous fluid used in the damperconsisted of Polydimethylsiloxane, a silicone oil with a veryhigh kinematic viscosity of 100,000 centistokes. The dynamicviscosity of the oil is 100 Pa-s. For comparison, the dynamicviscosity of water is 1 mPa-s. The oil displays a characteristicnon-newtonian behavior, with the apparent reduction in viscosityas the shear rate increases (known as shear thinning). To accountfor this change in viscosity, the damping torque calculationwas adjusted based on the shear-thinning data provided by themanufacturer [27] . In order to seal the fluid in the damper, anO-ring as well as a rotary shaft seal were incorporated betweenthe rotating assembly and the stationary housing (Fig. 3B).

DC Motor Coupler

Damper

Load Cell

FIGURE 4. Experimental setup for mechanical characterization of thedamper prototype. The housing of the damper prototype is connected toa load cell through a lever arm to measure the torque, and the shaft isdriven by the velocity-controlled DC motor.

2.3 Mechanical TestingA test setup was built for experimental characterization

of the prototype performance before testing the prostheticknee assembly on an above-knee amputee (Fig. 4). Avelocity-controlled DC motor (VexRobotics) was used to apply alinearly increasing velocity profile to the damper and a magneticencoder was used to record and control the angular velocity. Aload cell (Omega Engineering LC101-250) measured the forceexperienced by the damper at a fixed lever length. The velocitycontrol and the data collection was controlled on a Visual Basicplatform supported by VexRobotics.

In order to measure the torque velocity relationship, themotor applied a linearly increasing velocity profile up to themaximum angular velocity of 6 rad/sec. This limit was chosenbased on the largest knee angular velocities measured in theable-bodied human gait [17]. The experimental setup wasvalidated with two commercially available viscous dampers(ACE controls FDT-57 and FDT-63 [28]). The experimentallymeasured values matched the values provided by the data sheetfor both the dampers.

2.4 Preliminary Clinical Study in IndiaTo further validate the results of the design and

computational modeling, a preliminary, qualitative study wasconducted at the Jaipur-Foot clinic in Jaipur, India with oneabove-knee amputee [29]. The MIT Committee on the Useof Humans as Experimental Subjects approved the experimentprotocol. At the time of testing, the subject had been using asimple, single-axis knee for daily use, which was designed anddistributed by the Jaipur-foot organization.

The main goal of this study was to receive qualitativefeedback on the different damping conditions and observewhether there are visible differences in the gait for differentcases. The subject was tested with four different casesof damping coefficients, with zero, low, optimal, and highmagnitudes. The relevant human body parameters of the subject(Table 1) were used for calculating the damper coefficients,as previously discussed in the computational modeling andanalysis section. The low, optimal, and high magnitudes ofthe damping coefficients for the subject were estimated as Blow

Gender Male

Weight (kg) 75

Knee-axis to the ground height (cm) 49

Foot size (cm) 28

TABLE 1. Body parameters of the subject (Fig. 5), which were usedfor modeling and design of the damper prototypes



FIGURE 5. Subject wearing the knee prosthesis with the damperprototype. The knee prosthesis was attached to the socket, whichinterfaces with the residual limb and the pylon, which interfaces withthe prosthetic foot.

= 0.8 N-m/(rad/s), Boptimal = 1.5 N-m/(rad/s), and Bhigh = 2.2N-m/(rad/s), respectively. The low and high coefficients werechosen to be 50% lower and higher than the optimal value. Threedifferent damper prototypes were constructed, with a differentnumber of interacting fins, n, as discussed in the previous section(Equation 3). The knee prosthesis used in the study was asingle-axis prosthetic knee designed by Arelekatti et al. [4]. Astandard single-part prosthetic foot designed by the Jaipur-footorganization was used [29], along with the standard pylon andsocket assembly (Fig. 5).

The testing protocol began by a fitment session of theprosthetic knee by a trained prosthetist (Fig. 5). After anacclimatization period, the subject was asked to walk for 10minutes with each of the four different damping conditions.Starting without a damper, the dampers were tested in the orderof increasing damping value (low, optimal, and high). Thesubject wasn’t told about which damper was being tested inorder to evaluate whether it was possible for the subject to detectthe difference between the three different dampers. Qualitativefeedback from the subject and the prosthetist was collected aftereach trial. Each trial was video-recorded with an iPhone camera.

3 RESULTS3.1 Mechanical Testing

The results of mechanical testing of each of the threedampers (low, optimal, and high) are shown in Fig. 6. The

0 1 2 3 4 5 6Angular Velocity (rad/s)

0

5

10

15

Dam

ping

Torq

ue (N

*m) Low damper (computed): 0.8 Nm/(rad/s)

Optimal damper (computed): 1.5 Nm/(rad/s)High damper (computed): 2.2 Nm/(rad/s)Low damper (experiment)Optimal damper (experiment)High damper (experiment)

FIGURE 6. The three dampers were mechanically tested over alinearly increasing velocity range

theoretically calculated values of damping torque in the design(Equation 3) were found to be larger than the experimentalmeasurements by over 20% at the highest angular velocity (6rad/s). However, at lower velocities up to 3 rad/s, there wasless than 10% difference. One of the possible causes of thisbehavior was the porous nature of the 3D printed fin structures.The pores could provide an alternative flow path for the Siliconeoil due to high shearing forces. In addition, the dampers werefilled with silicone oil by hand. In the absence of a concealedvacuum chamber, the silicone oil absorbs ambient air leadingto bubble entrapments which can reduce the effective viscosityof the fluid. Additionally, because of the linearly increasingangular velocity profile, the oil may have warmed up, alteringit’s viscosity. Despite the error, the theoretical calculation wasfound to be an extremely useful design tool to size the damperprototype before empirical characterization through mechanicaltesting.

3.2 Preliminary Clinical Study in IndiaAfter an acclimatization period of 10 minutes, the subject

was able to walk with the knee prosthesis comfortably (Fig.7A). The subject was able to identify the three different dampingvalues as low, medium, and high without explicit suggestions orprompts.

There was an observable difference in the peak knee-flexionangle that was observed between the four different test cases(Fig. 7B-E). The high damping case prevented proper toeclearance, as the subject was unable to flex the knee far enoughto clear the ground. Moreover, the high damping case was theonly case where the subject reported the need to concentrateand exert extra muscular effort to ensure smooth stance to swingtransition. The subject also reported negligible change between



No Damper, Peak knee

flexion angle = 72°

A

B C D E

Low Damping, 60° Optimal Damping, 44° High Damping, 36°

FIGURE 7. A. The subject walking comfortably after acclimatization, snapshots through a full gait cycle are shown (read left to right). There is nodamping module attached. B-E. The approximate values of peak flexion angle through the swing phase were calculated using the image processingtoolbox on MATLAB.

the no-damping case and the low-damping case, as there waslittle resistance on offer in the damper. The optimal case damperwas perceived by the subject as the most comfortable one,offering smooth transition and minimal conscious effort to useit. This confirmed the predicted optimal case damper as the bestof the three damping coefficients. However, a full clinical gaitanalysis with motion capture cameras and ground reaction forceplates is yet to be carried out, which will provide more accurateinformation about the kinematic performance under differentdamping conditions.

4 DISCUSSION4.1 Comparison with Traditional Fluid Dampers

The most common fluid dampers used in prosthetic kneesare linear hydraulic cylinders, which are made of a pistonand two chambers [20]. The damping force is the result ofpressurized flow of a viscous fluid from one chamber to the

other through a small orifice, usually adjustable in diameter.This necessitates the use of a hydraulic accumulator, which canaccommodate the changes in volume to keep the fluid insidecompletely pressurized. These features have tight tolerances,requiring expensive manufacturing processes. In the absence ofhigh-quality manufacturing, the seal between the two chamberscan break down due to repeated sliding, leading to frequentleaks and seal failures. Additionally, the damping force isproportional to the square of the piston velocity, leading to anon-linear dependence which can be uncomfortable for amputeeswith sudden cadence changes. The linear hydraulic cylindersalso require an additional linkage between the rotating elements.

The rotary, shear-based architecture of hydraulic dampersovercomes these challenges on most fronts. It is very simple tointegrate within the knee system as it can be mounted coaxially.It provides a predictable, linear dependence to gait cadence andconsists of only one dynamic seal on a shaft, which is rotating(and not sliding). The seal can be mounted close to the axis



to reduce the friction torque on the seals, mitigating the sealwear. They can also be made very compact by the use ofhigh-viscosity liquids, such as silicone oils, which are very safeto use and are available worldwide at competitive prices due totheir widespread use in cosmetics and industry.

4.2 Using Kinematic Data Input from Below-kneeAmputees

The behavior of the foot prosthesis should be accountedtowards any attempt to replicate able-bodied kinematics forabove-knee amputees [1]. Passive prosthetic feet cannot enablethe ankle plantar-flexion required during the transition fromstance to swing [17], altering the kinematics of below-kneeamputees. Therefore, this study used the experimental kinematicdata from a study that implemented a fully characterized passivefoot to reduce the kinematic error in the lower-leg trajectoryof below-knee amputees. We hypothesize that using a fullyoptimized passive foot in association with an optimized kneemodule will reduce the overall trajectory error of the lower leg.The hypothesis may be novel, but needs to be supported byfurther evidence through experimental investigations [24].

4.3 Limitations and Future WorkA complete quantitative, clinical gait-analysis of multiple

subjects would be required to quantify the performance of thedifferent damping magnitudes empirically. This would involvecollecting marker data using motion capture systems along withground reaction force data. This experiment is ongoing and theresults are expected to be more conclusive than the results ofqualitative user-testing presented in this study. The qualitativeclinical study was done in conjunction with a passive foot usedby Jaipur-foot, which was not characterized in the analysis ofthis study. In future, a fully optimized leg assembly withan optimized prosthetic knee and an optimized prosthetic footsuch as the U-spring foot would be relevant. Furthermore,this study used kinematic data only from one subject and theuser-centric study also involved only one subject. Data from alarge sample of subjects and testing on an equally large sample ofsubjects spanning different body parameters would be necessaryto conclusively establish insights, which could be used by otherprosthesis designers and researchers.

The rotor and stator fins in the prototype were made of 3Dprinted plastic (ABS), which is porous and has low strengthproperties. In the future, these parts could be substituted withstronger materials such as molded plastic. The resulting additionin strength could aid in the making the design more compactby the addition of more fins in the same amount of space.Streamlining the liquid filling process in the damper with suctionwould need to be devised to ensure that there is minimal bubbleentrapment. Additionally, a detailed cost and manufacturinganalysis would be necessary to clarify the advantage of the

rotary, shear-based hydraulic damping architecture. Localmanufacturing in developing countries will also need to beconsidered for a complete comparison in terms of affordabilityof damping products in a global market.

ACKNOWLEDGEMENTWe would like to acknowledge Dr. Pooja Mukul and the

rest of the staff at Bhagwan Mahaveer Viklang Sahayata Samiti(BMVSS, a.k.a., the Jaipur-Foot Organization, Jaipur, India)for their partnership in our work. Funding for this study wasprovided by the the Tata Center for Technology and Design atMIT, the National Science Foundation Graduate CAREER Grant(no. 1653758), and the Indo-US NIH collaborative programgrant on affordable medical devices (no. 9208498).

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